Properties

Label 405.4.e.k.271.1
Level $405$
Weight $4$
Character 405.271
Analytic conductor $23.896$
Analytic rank $0$
Dimension $2$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [405,4,Mod(136,405)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(405, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("405.136");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 405.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(23.8957735523\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 15)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 271.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 405.271
Dual form 405.4.e.k.136.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.50000 + 2.59808i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(-10.0000 - 17.3205i) q^{7} +21.0000 q^{8} +O(q^{10})\) \(q+(1.50000 + 2.59808i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(-10.0000 - 17.3205i) q^{7} +21.0000 q^{8} -15.0000 q^{10} +(-12.0000 - 20.7846i) q^{11} +(-37.0000 + 64.0859i) q^{13} +(30.0000 - 51.9615i) q^{14} +(35.5000 + 61.4878i) q^{16} -54.0000 q^{17} -124.000 q^{19} +(-2.50000 - 4.33013i) q^{20} +(36.0000 - 62.3538i) q^{22} +(-60.0000 + 103.923i) q^{23} +(-12.5000 - 21.6506i) q^{25} -222.000 q^{26} +20.0000 q^{28} +(-39.0000 - 67.5500i) q^{29} +(-100.000 + 173.205i) q^{31} +(-22.5000 + 38.9711i) q^{32} +(-81.0000 - 140.296i) q^{34} +100.000 q^{35} -70.0000 q^{37} +(-186.000 - 322.161i) q^{38} +(-52.5000 + 90.9327i) q^{40} +(165.000 - 285.788i) q^{41} +(-46.0000 - 79.6743i) q^{43} +24.0000 q^{44} -360.000 q^{46} +(-12.0000 - 20.7846i) q^{47} +(-28.5000 + 49.3634i) q^{49} +(37.5000 - 64.9519i) q^{50} +(-37.0000 - 64.0859i) q^{52} -450.000 q^{53} +120.000 q^{55} +(-210.000 - 363.731i) q^{56} +(117.000 - 202.650i) q^{58} +(12.0000 - 20.7846i) q^{59} +(161.000 + 278.860i) q^{61} -600.000 q^{62} +433.000 q^{64} +(-185.000 - 320.429i) q^{65} +(98.0000 - 169.741i) q^{67} +(27.0000 - 46.7654i) q^{68} +(150.000 + 259.808i) q^{70} +288.000 q^{71} -430.000 q^{73} +(-105.000 - 181.865i) q^{74} +(62.0000 - 107.387i) q^{76} +(-240.000 + 415.692i) q^{77} +(260.000 + 450.333i) q^{79} -355.000 q^{80} +990.000 q^{82} +(78.0000 + 135.100i) q^{83} +(135.000 - 233.827i) q^{85} +(138.000 - 239.023i) q^{86} +(-252.000 - 436.477i) q^{88} -1026.00 q^{89} +1480.00 q^{91} +(-60.0000 - 103.923i) q^{92} +(36.0000 - 62.3538i) q^{94} +(310.000 - 536.936i) q^{95} +(143.000 + 247.683i) q^{97} -171.000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 3 q^{2} - q^{4} - 5 q^{5} - 20 q^{7} + 42 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 3 q^{2} - q^{4} - 5 q^{5} - 20 q^{7} + 42 q^{8} - 30 q^{10} - 24 q^{11} - 74 q^{13} + 60 q^{14} + 71 q^{16} - 108 q^{17} - 248 q^{19} - 5 q^{20} + 72 q^{22} - 120 q^{23} - 25 q^{25} - 444 q^{26} + 40 q^{28} - 78 q^{29} - 200 q^{31} - 45 q^{32} - 162 q^{34} + 200 q^{35} - 140 q^{37} - 372 q^{38} - 105 q^{40} + 330 q^{41} - 92 q^{43} + 48 q^{44} - 720 q^{46} - 24 q^{47} - 57 q^{49} + 75 q^{50} - 74 q^{52} - 900 q^{53} + 240 q^{55} - 420 q^{56} + 234 q^{58} + 24 q^{59} + 322 q^{61} - 1200 q^{62} + 866 q^{64} - 370 q^{65} + 196 q^{67} + 54 q^{68} + 300 q^{70} + 576 q^{71} - 860 q^{73} - 210 q^{74} + 124 q^{76} - 480 q^{77} + 520 q^{79} - 710 q^{80} + 1980 q^{82} + 156 q^{83} + 270 q^{85} + 276 q^{86} - 504 q^{88} - 2052 q^{89} + 2960 q^{91} - 120 q^{92} + 72 q^{94} + 620 q^{95} + 286 q^{97} - 342 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.50000 + 2.59808i 0.530330 + 0.918559i 0.999374 + 0.0353837i \(0.0112653\pi\)
−0.469044 + 0.883175i \(0.655401\pi\)
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.0625000 + 0.108253i
\(5\) −2.50000 + 4.33013i −0.223607 + 0.387298i
\(6\) 0 0
\(7\) −10.0000 17.3205i −0.539949 0.935220i −0.998906 0.0467610i \(-0.985110\pi\)
0.458957 0.888459i \(-0.348223\pi\)
\(8\) 21.0000 0.928078
\(9\) 0 0
\(10\) −15.0000 −0.474342
\(11\) −12.0000 20.7846i −0.328921 0.569709i 0.653377 0.757033i \(-0.273352\pi\)
−0.982298 + 0.187324i \(0.940018\pi\)
\(12\) 0 0
\(13\) −37.0000 + 64.0859i −0.789381 + 1.36725i 0.136966 + 0.990576i \(0.456265\pi\)
−0.926347 + 0.376672i \(0.877068\pi\)
\(14\) 30.0000 51.9615i 0.572703 0.991950i
\(15\) 0 0
\(16\) 35.5000 + 61.4878i 0.554688 + 0.960747i
\(17\) −54.0000 −0.770407 −0.385204 0.922832i \(-0.625869\pi\)
−0.385204 + 0.922832i \(0.625869\pi\)
\(18\) 0 0
\(19\) −124.000 −1.49724 −0.748620 0.663000i \(-0.769283\pi\)
−0.748620 + 0.663000i \(0.769283\pi\)
\(20\) −2.50000 4.33013i −0.0279508 0.0484123i
\(21\) 0 0
\(22\) 36.0000 62.3538i 0.348874 0.604267i
\(23\) −60.0000 + 103.923i −0.543951 + 0.942150i 0.454721 + 0.890634i \(0.349739\pi\)
−0.998672 + 0.0515165i \(0.983595\pi\)
\(24\) 0 0
\(25\) −12.5000 21.6506i −0.100000 0.173205i
\(26\) −222.000 −1.67453
\(27\) 0 0
\(28\) 20.0000 0.134987
\(29\) −39.0000 67.5500i −0.249728 0.432542i 0.713722 0.700429i \(-0.247008\pi\)
−0.963450 + 0.267887i \(0.913675\pi\)
\(30\) 0 0
\(31\) −100.000 + 173.205i −0.579372 + 1.00350i 0.416180 + 0.909282i \(0.363369\pi\)
−0.995551 + 0.0942192i \(0.969965\pi\)
\(32\) −22.5000 + 38.9711i −0.124296 + 0.215287i
\(33\) 0 0
\(34\) −81.0000 140.296i −0.408570 0.707664i
\(35\) 100.000 0.482945
\(36\) 0 0
\(37\) −70.0000 −0.311025 −0.155513 0.987834i \(-0.549703\pi\)
−0.155513 + 0.987834i \(0.549703\pi\)
\(38\) −186.000 322.161i −0.794031 1.37530i
\(39\) 0 0
\(40\) −52.5000 + 90.9327i −0.207524 + 0.359443i
\(41\) 165.000 285.788i 0.628504 1.08860i −0.359348 0.933204i \(-0.617001\pi\)
0.987852 0.155397i \(-0.0496658\pi\)
\(42\) 0 0
\(43\) −46.0000 79.6743i −0.163138 0.282563i 0.772854 0.634583i \(-0.218828\pi\)
−0.935992 + 0.352020i \(0.885495\pi\)
\(44\) 24.0000 0.0822304
\(45\) 0 0
\(46\) −360.000 −1.15389
\(47\) −12.0000 20.7846i −0.0372421 0.0645053i 0.846804 0.531906i \(-0.178524\pi\)
−0.884046 + 0.467401i \(0.845191\pi\)
\(48\) 0 0
\(49\) −28.5000 + 49.3634i −0.0830904 + 0.143917i
\(50\) 37.5000 64.9519i 0.106066 0.183712i
\(51\) 0 0
\(52\) −37.0000 64.0859i −0.0986726 0.170906i
\(53\) −450.000 −1.16627 −0.583134 0.812376i \(-0.698174\pi\)
−0.583134 + 0.812376i \(0.698174\pi\)
\(54\) 0 0
\(55\) 120.000 0.294196
\(56\) −210.000 363.731i −0.501115 0.867956i
\(57\) 0 0
\(58\) 117.000 202.650i 0.264877 0.458780i
\(59\) 12.0000 20.7846i 0.0264791 0.0458631i −0.852482 0.522756i \(-0.824904\pi\)
0.878961 + 0.476893i \(0.158237\pi\)
\(60\) 0 0
\(61\) 161.000 + 278.860i 0.337933 + 0.585318i 0.984044 0.177926i \(-0.0569388\pi\)
−0.646110 + 0.763244i \(0.723605\pi\)
\(62\) −600.000 −1.22903
\(63\) 0 0
\(64\) 433.000 0.845703
\(65\) −185.000 320.429i −0.353022 0.611452i
\(66\) 0 0
\(67\) 98.0000 169.741i 0.178696 0.309510i −0.762738 0.646707i \(-0.776146\pi\)
0.941434 + 0.337197i \(0.109479\pi\)
\(68\) 27.0000 46.7654i 0.0481505 0.0833990i
\(69\) 0 0
\(70\) 150.000 + 259.808i 0.256120 + 0.443614i
\(71\) 288.000 0.481399 0.240699 0.970600i \(-0.422623\pi\)
0.240699 + 0.970600i \(0.422623\pi\)
\(72\) 0 0
\(73\) −430.000 −0.689420 −0.344710 0.938709i \(-0.612023\pi\)
−0.344710 + 0.938709i \(0.612023\pi\)
\(74\) −105.000 181.865i −0.164946 0.285695i
\(75\) 0 0
\(76\) 62.0000 107.387i 0.0935775 0.162081i
\(77\) −240.000 + 415.692i −0.355202 + 0.615228i
\(78\) 0 0
\(79\) 260.000 + 450.333i 0.370282 + 0.641347i 0.989609 0.143786i \(-0.0459277\pi\)
−0.619327 + 0.785133i \(0.712594\pi\)
\(80\) −355.000 −0.496128
\(81\) 0 0
\(82\) 990.000 1.33326
\(83\) 78.0000 + 135.100i 0.103152 + 0.178664i 0.912982 0.408001i \(-0.133774\pi\)
−0.809830 + 0.586665i \(0.800441\pi\)
\(84\) 0 0
\(85\) 135.000 233.827i 0.172268 0.298377i
\(86\) 138.000 239.023i 0.173034 0.299704i
\(87\) 0 0
\(88\) −252.000 436.477i −0.305265 0.528734i
\(89\) −1026.00 −1.22198 −0.610988 0.791640i \(-0.709227\pi\)
−0.610988 + 0.791640i \(0.709227\pi\)
\(90\) 0 0
\(91\) 1480.00 1.70490
\(92\) −60.0000 103.923i −0.0679938 0.117769i
\(93\) 0 0
\(94\) 36.0000 62.3538i 0.0395012 0.0684182i
\(95\) 310.000 536.936i 0.334793 0.579878i
\(96\) 0 0
\(97\) 143.000 + 247.683i 0.149685 + 0.259262i 0.931111 0.364736i \(-0.118841\pi\)
−0.781426 + 0.623998i \(0.785507\pi\)
\(98\) −171.000 −0.176261
\(99\) 0 0
\(100\) 25.0000 0.0250000
\(101\) −867.000 1501.69i −0.854156 1.47944i −0.877426 0.479712i \(-0.840741\pi\)
0.0232704 0.999729i \(-0.492592\pi\)
\(102\) 0 0
\(103\) −226.000 + 391.443i −0.216198 + 0.374467i −0.953643 0.300941i \(-0.902699\pi\)
0.737444 + 0.675408i \(0.236032\pi\)
\(104\) −777.000 + 1345.80i −0.732607 + 1.26891i
\(105\) 0 0
\(106\) −675.000 1169.13i −0.618508 1.07129i
\(107\) 1404.00 1.26850 0.634251 0.773127i \(-0.281308\pi\)
0.634251 + 0.773127i \(0.281308\pi\)
\(108\) 0 0
\(109\) −1474.00 −1.29526 −0.647631 0.761954i \(-0.724240\pi\)
−0.647631 + 0.761954i \(0.724240\pi\)
\(110\) 180.000 + 311.769i 0.156021 + 0.270237i
\(111\) 0 0
\(112\) 710.000 1229.76i 0.599006 1.03751i
\(113\) 543.000 940.504i 0.452046 0.782966i −0.546467 0.837480i \(-0.684028\pi\)
0.998513 + 0.0545145i \(0.0173611\pi\)
\(114\) 0 0
\(115\) −300.000 519.615i −0.243262 0.421342i
\(116\) 78.0000 0.0624321
\(117\) 0 0
\(118\) 72.0000 0.0561707
\(119\) 540.000 + 935.307i 0.415981 + 0.720500i
\(120\) 0 0
\(121\) 377.500 653.849i 0.283621 0.491247i
\(122\) −483.000 + 836.581i −0.358433 + 0.620823i
\(123\) 0 0
\(124\) −100.000 173.205i −0.0724215 0.125438i
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) 1244.00 0.869190 0.434595 0.900626i \(-0.356891\pi\)
0.434595 + 0.900626i \(0.356891\pi\)
\(128\) 829.500 + 1436.74i 0.572798 + 0.992115i
\(129\) 0 0
\(130\) 555.000 961.288i 0.374436 0.648543i
\(131\) 1164.00 2016.11i 0.776329 1.34464i −0.157715 0.987485i \(-0.550413\pi\)
0.934044 0.357157i \(-0.116254\pi\)
\(132\) 0 0
\(133\) 1240.00 + 2147.74i 0.808433 + 1.40025i
\(134\) 588.000 0.379071
\(135\) 0 0
\(136\) −1134.00 −0.714998
\(137\) 1059.00 + 1834.24i 0.660412 + 1.14387i 0.980507 + 0.196482i \(0.0629518\pi\)
−0.320095 + 0.947385i \(0.603715\pi\)
\(138\) 0 0
\(139\) −1162.00 + 2012.64i −0.709062 + 1.22813i 0.256144 + 0.966639i \(0.417548\pi\)
−0.965206 + 0.261492i \(0.915785\pi\)
\(140\) −50.0000 + 86.6025i −0.0301841 + 0.0522804i
\(141\) 0 0
\(142\) 432.000 + 748.246i 0.255300 + 0.442193i
\(143\) 1776.00 1.03858
\(144\) 0 0
\(145\) 390.000 0.223364
\(146\) −645.000 1117.17i −0.365620 0.633273i
\(147\) 0 0
\(148\) 35.0000 60.6218i 0.0194391 0.0336695i
\(149\) 129.000 223.435i 0.0709268 0.122849i −0.828381 0.560165i \(-0.810738\pi\)
0.899308 + 0.437316i \(0.144071\pi\)
\(150\) 0 0
\(151\) 404.000 + 699.749i 0.217729 + 0.377117i 0.954113 0.299446i \(-0.0968018\pi\)
−0.736384 + 0.676563i \(0.763468\pi\)
\(152\) −2604.00 −1.38955
\(153\) 0 0
\(154\) −1440.00 −0.753497
\(155\) −500.000 866.025i −0.259103 0.448780i
\(156\) 0 0
\(157\) −1189.00 + 2059.41i −0.604411 + 1.04687i 0.387733 + 0.921772i \(0.373258\pi\)
−0.992144 + 0.125099i \(0.960075\pi\)
\(158\) −780.000 + 1351.00i −0.392743 + 0.680252i
\(159\) 0 0
\(160\) −112.500 194.856i −0.0555869 0.0962794i
\(161\) 2400.00 1.17482
\(162\) 0 0
\(163\) −52.0000 −0.0249874 −0.0124937 0.999922i \(-0.503977\pi\)
−0.0124937 + 0.999922i \(0.503977\pi\)
\(164\) 165.000 + 285.788i 0.0785630 + 0.136075i
\(165\) 0 0
\(166\) −234.000 + 405.300i −0.109409 + 0.189502i
\(167\) −1860.00 + 3221.61i −0.861863 + 1.49279i 0.00826564 + 0.999966i \(0.497369\pi\)
−0.870129 + 0.492825i \(0.835964\pi\)
\(168\) 0 0
\(169\) −1639.50 2839.70i −0.746245 1.29253i
\(170\) 810.000 0.365436
\(171\) 0 0
\(172\) 92.0000 0.0407845
\(173\) 213.000 + 368.927i 0.0936075 + 0.162133i 0.909027 0.416738i \(-0.136827\pi\)
−0.815419 + 0.578871i \(0.803493\pi\)
\(174\) 0 0
\(175\) −250.000 + 433.013i −0.107990 + 0.187044i
\(176\) 852.000 1475.71i 0.364897 0.632021i
\(177\) 0 0
\(178\) −1539.00 2665.63i −0.648050 1.12246i
\(179\) 1440.00 0.601289 0.300644 0.953736i \(-0.402798\pi\)
0.300644 + 0.953736i \(0.402798\pi\)
\(180\) 0 0
\(181\) −3130.00 −1.28537 −0.642683 0.766133i \(-0.722179\pi\)
−0.642683 + 0.766133i \(0.722179\pi\)
\(182\) 2220.00 + 3845.15i 0.904161 + 1.56605i
\(183\) 0 0
\(184\) −1260.00 + 2182.38i −0.504828 + 0.874389i
\(185\) 175.000 303.109i 0.0695473 0.120460i
\(186\) 0 0
\(187\) 648.000 + 1122.37i 0.253403 + 0.438908i
\(188\) 24.0000 0.00931053
\(189\) 0 0
\(190\) 1860.00 0.710203
\(191\) 1788.00 + 3096.91i 0.677357 + 1.17322i 0.975774 + 0.218781i \(0.0702080\pi\)
−0.298417 + 0.954436i \(0.596459\pi\)
\(192\) 0 0
\(193\) −1333.00 + 2308.82i −0.497158 + 0.861102i −0.999995 0.00327888i \(-0.998956\pi\)
0.502837 + 0.864381i \(0.332290\pi\)
\(194\) −429.000 + 743.050i −0.158765 + 0.274989i
\(195\) 0 0
\(196\) −28.5000 49.3634i −0.0103863 0.0179896i
\(197\) 2718.00 0.982992 0.491496 0.870880i \(-0.336450\pi\)
0.491496 + 0.870880i \(0.336450\pi\)
\(198\) 0 0
\(199\) −3832.00 −1.36504 −0.682521 0.730866i \(-0.739116\pi\)
−0.682521 + 0.730866i \(0.739116\pi\)
\(200\) −262.500 454.663i −0.0928078 0.160748i
\(201\) 0 0
\(202\) 2601.00 4505.06i 0.905969 1.56918i
\(203\) −780.000 + 1351.00i −0.269681 + 0.467101i
\(204\) 0 0
\(205\) 825.000 + 1428.94i 0.281076 + 0.486837i
\(206\) −1356.00 −0.458626
\(207\) 0 0
\(208\) −5254.00 −1.75144
\(209\) 1488.00 + 2577.29i 0.492474 + 0.852990i
\(210\) 0 0
\(211\) −550.000 + 952.628i −0.179448 + 0.310813i −0.941692 0.336477i \(-0.890765\pi\)
0.762244 + 0.647290i \(0.224098\pi\)
\(212\) 225.000 389.711i 0.0728918 0.126252i
\(213\) 0 0
\(214\) 2106.00 + 3647.70i 0.672725 + 1.16519i
\(215\) 460.000 0.145915
\(216\) 0 0
\(217\) 4000.00 1.25133
\(218\) −2211.00 3829.56i −0.686917 1.18977i
\(219\) 0 0
\(220\) −60.0000 + 103.923i −0.0183873 + 0.0318477i
\(221\) 1998.00 3460.64i 0.608145 1.05334i
\(222\) 0 0
\(223\) −982.000 1700.87i −0.294886 0.510758i 0.680072 0.733145i \(-0.261948\pi\)
−0.974958 + 0.222387i \(0.928615\pi\)
\(224\) 900.000 0.268454
\(225\) 0 0
\(226\) 3258.00 0.958933
\(227\) 330.000 + 571.577i 0.0964884 + 0.167123i 0.910229 0.414106i \(-0.135906\pi\)
−0.813740 + 0.581228i \(0.802572\pi\)
\(228\) 0 0
\(229\) 953.000 1650.64i 0.275004 0.476322i −0.695132 0.718882i \(-0.744654\pi\)
0.970136 + 0.242561i \(0.0779873\pi\)
\(230\) 900.000 1558.85i 0.258018 0.446901i
\(231\) 0 0
\(232\) −819.000 1418.55i −0.231767 0.401433i
\(233\) 1458.00 0.409943 0.204972 0.978768i \(-0.434290\pi\)
0.204972 + 0.978768i \(0.434290\pi\)
\(234\) 0 0
\(235\) 120.000 0.0333104
\(236\) 12.0000 + 20.7846i 0.00330989 + 0.00573289i
\(237\) 0 0
\(238\) −1620.00 + 2805.92i −0.441214 + 0.764206i
\(239\) 588.000 1018.45i 0.159140 0.275639i −0.775419 0.631448i \(-0.782461\pi\)
0.934559 + 0.355808i \(0.115794\pi\)
\(240\) 0 0
\(241\) −433.000 749.978i −0.115734 0.200458i 0.802339 0.596869i \(-0.203589\pi\)
−0.918073 + 0.396411i \(0.870255\pi\)
\(242\) 2265.00 0.601652
\(243\) 0 0
\(244\) −322.000 −0.0844834
\(245\) −142.500 246.817i −0.0371591 0.0643615i
\(246\) 0 0
\(247\) 4588.00 7946.65i 1.18189 2.04710i
\(248\) −2100.00 + 3637.31i −0.537702 + 0.931327i
\(249\) 0 0
\(250\) 187.500 + 324.760i 0.0474342 + 0.0821584i
\(251\) −432.000 −0.108636 −0.0543179 0.998524i \(-0.517298\pi\)
−0.0543179 + 0.998524i \(0.517298\pi\)
\(252\) 0 0
\(253\) 2880.00 0.715668
\(254\) 1866.00 + 3232.01i 0.460958 + 0.798402i
\(255\) 0 0
\(256\) −756.500 + 1310.30i −0.184692 + 0.319897i
\(257\) 1263.00 2187.58i 0.306552 0.530963i −0.671054 0.741409i \(-0.734158\pi\)
0.977606 + 0.210445i \(0.0674914\pi\)
\(258\) 0 0
\(259\) 700.000 + 1212.44i 0.167938 + 0.290877i
\(260\) 370.000 0.0882555
\(261\) 0 0
\(262\) 6984.00 1.64684
\(263\) 2724.00 + 4718.11i 0.638666 + 1.10620i 0.985726 + 0.168358i \(0.0538466\pi\)
−0.347060 + 0.937843i \(0.612820\pi\)
\(264\) 0 0
\(265\) 1125.00 1948.56i 0.260786 0.451694i
\(266\) −3720.00 + 6443.23i −0.857473 + 1.48519i
\(267\) 0 0
\(268\) 98.0000 + 169.741i 0.0223370 + 0.0386887i
\(269\) 2574.00 0.583418 0.291709 0.956507i \(-0.405776\pi\)
0.291709 + 0.956507i \(0.405776\pi\)
\(270\) 0 0
\(271\) −3184.00 −0.713706 −0.356853 0.934161i \(-0.616150\pi\)
−0.356853 + 0.934161i \(0.616150\pi\)
\(272\) −1917.00 3320.34i −0.427335 0.740166i
\(273\) 0 0
\(274\) −3177.00 + 5502.73i −0.700473 + 1.21325i
\(275\) −300.000 + 519.615i −0.0657843 + 0.113942i
\(276\) 0 0
\(277\) −1981.00 3431.19i −0.429699 0.744261i 0.567147 0.823617i \(-0.308047\pi\)
−0.996846 + 0.0793553i \(0.974714\pi\)
\(278\) −6972.00 −1.50415
\(279\) 0 0
\(280\) 2100.00 0.448211
\(281\) −4143.00 7175.89i −0.879540 1.52341i −0.851847 0.523791i \(-0.824517\pi\)
−0.0276929 0.999616i \(-0.508816\pi\)
\(282\) 0 0
\(283\) 1358.00 2352.12i 0.285246 0.494061i −0.687423 0.726258i \(-0.741258\pi\)
0.972669 + 0.232197i \(0.0745912\pi\)
\(284\) −144.000 + 249.415i −0.0300874 + 0.0521129i
\(285\) 0 0
\(286\) 2664.00 + 4614.18i 0.550789 + 0.953994i
\(287\) −6600.00 −1.35744
\(288\) 0 0
\(289\) −1997.00 −0.406473
\(290\) 585.000 + 1013.25i 0.118456 + 0.205173i
\(291\) 0 0
\(292\) 215.000 372.391i 0.0430888 0.0746320i
\(293\) 3009.00 5211.74i 0.599958 1.03916i −0.392869 0.919595i \(-0.628517\pi\)
0.992827 0.119563i \(-0.0381493\pi\)
\(294\) 0 0
\(295\) 60.0000 + 103.923i 0.0118418 + 0.0205106i
\(296\) −1470.00 −0.288655
\(297\) 0 0
\(298\) 774.000 0.150458
\(299\) −4440.00 7690.31i −0.858769 1.48743i
\(300\) 0 0
\(301\) −920.000 + 1593.49i −0.176172 + 0.305140i
\(302\) −1212.00 + 2099.25i −0.230936 + 0.399993i
\(303\) 0 0
\(304\) −4402.00 7624.49i −0.830500 1.43847i
\(305\) −1610.00 −0.302257
\(306\) 0 0
\(307\) 9236.00 1.71702 0.858512 0.512793i \(-0.171389\pi\)
0.858512 + 0.512793i \(0.171389\pi\)
\(308\) −240.000 415.692i −0.0444002 0.0769034i
\(309\) 0 0
\(310\) 1500.00 2598.08i 0.274820 0.476003i
\(311\) 768.000 1330.22i 0.140030 0.242539i −0.787478 0.616343i \(-0.788613\pi\)
0.927508 + 0.373804i \(0.121947\pi\)
\(312\) 0 0
\(313\) 3671.00 + 6358.36i 0.662930 + 1.14823i 0.979842 + 0.199774i \(0.0640208\pi\)
−0.316912 + 0.948455i \(0.602646\pi\)
\(314\) −7134.00 −1.28215
\(315\) 0 0
\(316\) −520.000 −0.0925705
\(317\) −1947.00 3372.30i −0.344967 0.597500i 0.640381 0.768057i \(-0.278776\pi\)
−0.985348 + 0.170558i \(0.945443\pi\)
\(318\) 0 0
\(319\) −936.000 + 1621.20i −0.164282 + 0.284545i
\(320\) −1082.50 + 1874.94i −0.189105 + 0.327539i
\(321\) 0 0
\(322\) 3600.00 + 6235.38i 0.623044 + 1.07914i
\(323\) 6696.00 1.15348
\(324\) 0 0
\(325\) 1850.00 0.315752
\(326\) −78.0000 135.100i −0.0132516 0.0229524i
\(327\) 0 0
\(328\) 3465.00 6001.56i 0.583301 1.01031i
\(329\) −240.000 + 415.692i −0.0402177 + 0.0696591i
\(330\) 0 0
\(331\) −1846.00 3197.37i −0.306542 0.530946i 0.671062 0.741402i \(-0.265839\pi\)
−0.977603 + 0.210456i \(0.932505\pi\)
\(332\) −156.000 −0.0257880
\(333\) 0 0
\(334\) −11160.0 −1.82829
\(335\) 490.000 + 848.705i 0.0799151 + 0.138417i
\(336\) 0 0
\(337\) 4499.00 7792.50i 0.727229 1.25960i −0.230821 0.972996i \(-0.574141\pi\)
0.958050 0.286601i \(-0.0925255\pi\)
\(338\) 4918.50 8519.09i 0.791512 1.37094i
\(339\) 0 0
\(340\) 135.000 + 233.827i 0.0215335 + 0.0372972i
\(341\) 4800.00 0.762271
\(342\) 0 0
\(343\) −5720.00 −0.900440
\(344\) −966.000 1673.16i −0.151405 0.262241i
\(345\) 0 0
\(346\) −639.000 + 1106.78i −0.0992857 + 0.171968i
\(347\) 2622.00 4541.44i 0.405638 0.702585i −0.588758 0.808310i \(-0.700383\pi\)
0.994395 + 0.105724i \(0.0337161\pi\)
\(348\) 0 0
\(349\) −3151.00 5457.69i −0.483293 0.837088i 0.516523 0.856273i \(-0.327226\pi\)
−0.999816 + 0.0191856i \(0.993893\pi\)
\(350\) −1500.00 −0.229081
\(351\) 0 0
\(352\) 1080.00 0.163535
\(353\) 1707.00 + 2956.61i 0.257378 + 0.445792i 0.965539 0.260259i \(-0.0838081\pi\)
−0.708161 + 0.706051i \(0.750475\pi\)
\(354\) 0 0
\(355\) −720.000 + 1247.08i −0.107644 + 0.186445i
\(356\) 513.000 888.542i 0.0763734 0.132283i
\(357\) 0 0
\(358\) 2160.00 + 3741.23i 0.318881 + 0.552319i
\(359\) −4824.00 −0.709195 −0.354597 0.935019i \(-0.615382\pi\)
−0.354597 + 0.935019i \(0.615382\pi\)
\(360\) 0 0
\(361\) 8517.00 1.24173
\(362\) −4695.00 8131.98i −0.681668 1.18068i
\(363\) 0 0
\(364\) −740.000 + 1281.72i −0.106556 + 0.184561i
\(365\) 1075.00 1861.95i 0.154159 0.267011i
\(366\) 0 0
\(367\) 1754.00 + 3038.02i 0.249477 + 0.432107i 0.963381 0.268137i \(-0.0864080\pi\)
−0.713904 + 0.700244i \(0.753075\pi\)
\(368\) −8520.00 −1.20689
\(369\) 0 0
\(370\) 1050.00 0.147532
\(371\) 4500.00 + 7794.23i 0.629726 + 1.09072i
\(372\) 0 0
\(373\) −5401.00 + 9354.81i −0.749740 + 1.29859i 0.198207 + 0.980160i \(0.436488\pi\)
−0.947947 + 0.318428i \(0.896845\pi\)
\(374\) −1944.00 + 3367.11i −0.268775 + 0.465532i
\(375\) 0 0
\(376\) −252.000 436.477i −0.0345636 0.0598659i
\(377\) 5772.00 0.788523
\(378\) 0 0
\(379\) 1460.00 0.197876 0.0989382 0.995094i \(-0.468455\pi\)
0.0989382 + 0.995094i \(0.468455\pi\)
\(380\) 310.000 + 536.936i 0.0418491 + 0.0724848i
\(381\) 0 0
\(382\) −5364.00 + 9290.72i −0.718445 + 1.24438i
\(383\) −2436.00 + 4219.28i −0.324997 + 0.562911i −0.981512 0.191402i \(-0.938697\pi\)
0.656515 + 0.754313i \(0.272030\pi\)
\(384\) 0 0
\(385\) −1200.00 2078.46i −0.158851 0.275138i
\(386\) −7998.00 −1.05463
\(387\) 0 0
\(388\) −286.000 −0.0374213
\(389\) −7023.00 12164.2i −0.915373 1.58547i −0.806354 0.591434i \(-0.798562\pi\)
−0.109020 0.994040i \(-0.534771\pi\)
\(390\) 0 0
\(391\) 3240.00 5611.84i 0.419064 0.725839i
\(392\) −598.500 + 1036.63i −0.0771143 + 0.133566i
\(393\) 0 0
\(394\) 4077.00 + 7061.57i 0.521310 + 0.902936i
\(395\) −2600.00 −0.331190
\(396\) 0 0
\(397\) −2734.00 −0.345631 −0.172816 0.984954i \(-0.555286\pi\)
−0.172816 + 0.984954i \(0.555286\pi\)
\(398\) −5748.00 9955.83i −0.723923 1.25387i
\(399\) 0 0
\(400\) 887.500 1537.20i 0.110937 0.192149i
\(401\) −7971.00 + 13806.2i −0.992650 + 1.71932i −0.391520 + 0.920170i \(0.628051\pi\)
−0.601130 + 0.799151i \(0.705283\pi\)
\(402\) 0 0
\(403\) −7400.00 12817.2i −0.914690 1.58429i
\(404\) 1734.00 0.213539
\(405\) 0 0
\(406\) −4680.00 −0.572080
\(407\) 840.000 + 1454.92i 0.102303 + 0.177194i
\(408\) 0 0
\(409\) −4357.00 + 7546.55i −0.526748 + 0.912354i 0.472767 + 0.881188i \(0.343255\pi\)
−0.999514 + 0.0311660i \(0.990078\pi\)
\(410\) −2475.00 + 4286.83i −0.298126 + 0.516369i
\(411\) 0 0
\(412\) −226.000 391.443i −0.0270248 0.0468083i
\(413\) −480.000 −0.0571895
\(414\) 0 0
\(415\) −780.000 −0.0922619
\(416\) −1665.00 2883.86i −0.196234 0.339887i
\(417\) 0 0
\(418\) −4464.00 + 7731.87i −0.522348 + 0.904733i
\(419\) 5988.00 10371.5i 0.698169 1.20926i −0.270931 0.962599i \(-0.587332\pi\)
0.969101 0.246666i \(-0.0793351\pi\)
\(420\) 0 0
\(421\) −5527.00 9573.04i −0.639833 1.10822i −0.985469 0.169854i \(-0.945670\pi\)
0.345637 0.938368i \(-0.387663\pi\)
\(422\) −3300.00 −0.380667
\(423\) 0 0
\(424\) −9450.00 −1.08239
\(425\) 675.000 + 1169.13i 0.0770407 + 0.133438i
\(426\) 0 0
\(427\) 3220.00 5577.20i 0.364934 0.632084i
\(428\) −702.000 + 1215.90i −0.0792814 + 0.137319i
\(429\) 0 0
\(430\) 690.000 + 1195.12i 0.0773832 + 0.134032i
\(431\) −720.000 −0.0804668 −0.0402334 0.999190i \(-0.512810\pi\)
−0.0402334 + 0.999190i \(0.512810\pi\)
\(432\) 0 0
\(433\) −15622.0 −1.73382 −0.866912 0.498462i \(-0.833898\pi\)
−0.866912 + 0.498462i \(0.833898\pi\)
\(434\) 6000.00 + 10392.3i 0.663616 + 1.14942i
\(435\) 0 0
\(436\) 737.000 1276.52i 0.0809539 0.140216i
\(437\) 7440.00 12886.5i 0.814424 1.41062i
\(438\) 0 0
\(439\) 4940.00 + 8556.33i 0.537069 + 0.930231i 0.999060 + 0.0433464i \(0.0138019\pi\)
−0.461991 + 0.886885i \(0.652865\pi\)
\(440\) 2520.00 0.273037
\(441\) 0 0
\(442\) 11988.0 1.29007
\(443\) −8058.00 13956.9i −0.864215 1.49686i −0.867825 0.496870i \(-0.834482\pi\)
0.00361002 0.999993i \(-0.498851\pi\)
\(444\) 0 0
\(445\) 2565.00 4442.71i 0.273242 0.473269i
\(446\) 2946.00 5102.62i 0.312774 0.541740i
\(447\) 0 0
\(448\) −4330.00 7499.78i −0.456637 0.790918i
\(449\) −9018.00 −0.947852 −0.473926 0.880565i \(-0.657164\pi\)
−0.473926 + 0.880565i \(0.657164\pi\)
\(450\) 0 0
\(451\) −7920.00 −0.826914
\(452\) 543.000 + 940.504i 0.0565057 + 0.0978707i
\(453\) 0 0
\(454\) −990.000 + 1714.73i −0.102341 + 0.177261i
\(455\) −3700.00 + 6408.59i −0.381228 + 0.660306i
\(456\) 0 0
\(457\) 1835.00 + 3178.31i 0.187829 + 0.325329i 0.944526 0.328437i \(-0.106522\pi\)
−0.756697 + 0.653765i \(0.773188\pi\)
\(458\) 5718.00 0.583372
\(459\) 0 0
\(460\) 600.000 0.0608155
\(461\) 8781.00 + 15209.1i 0.887141 + 1.53657i 0.843240 + 0.537537i \(0.180645\pi\)
0.0439008 + 0.999036i \(0.486021\pi\)
\(462\) 0 0
\(463\) −586.000 + 1014.98i −0.0588202 + 0.101879i −0.893936 0.448195i \(-0.852067\pi\)
0.835116 + 0.550074i \(0.185401\pi\)
\(464\) 2769.00 4796.05i 0.277042 0.479851i
\(465\) 0 0
\(466\) 2187.00 + 3788.00i 0.217405 + 0.376557i
\(467\) −6876.00 −0.681335 −0.340667 0.940184i \(-0.610653\pi\)
−0.340667 + 0.940184i \(0.610653\pi\)
\(468\) 0 0
\(469\) −3920.00 −0.385946
\(470\) 180.000 + 311.769i 0.0176655 + 0.0305975i
\(471\) 0 0
\(472\) 252.000 436.477i 0.0245747 0.0425646i
\(473\) −1104.00 + 1912.18i −0.107319 + 0.185882i
\(474\) 0 0
\(475\) 1550.00 + 2684.68i 0.149724 + 0.259329i
\(476\) −1080.00 −0.103995
\(477\) 0 0
\(478\) 3528.00 0.337588
\(479\) 1140.00 + 1974.54i 0.108743 + 0.188349i 0.915261 0.402861i \(-0.131984\pi\)
−0.806518 + 0.591209i \(0.798651\pi\)
\(480\) 0 0
\(481\) 2590.00 4486.01i 0.245517 0.425248i
\(482\) 1299.00 2249.93i 0.122755 0.212618i
\(483\) 0 0
\(484\) 377.500 + 653.849i 0.0354527 + 0.0614058i
\(485\) −1430.00 −0.133882
\(486\) 0 0
\(487\) −3076.00 −0.286215 −0.143108 0.989707i \(-0.545710\pi\)
−0.143108 + 0.989707i \(0.545710\pi\)
\(488\) 3381.00 + 5856.06i 0.313628 + 0.543220i
\(489\) 0 0
\(490\) 427.500 740.452i 0.0394132 0.0682657i
\(491\) −9456.00 + 16378.3i −0.869131 + 1.50538i −0.00624491 + 0.999981i \(0.501988\pi\)
−0.862886 + 0.505398i \(0.831346\pi\)
\(492\) 0 0
\(493\) 2106.00 + 3647.70i 0.192392 + 0.333233i
\(494\) 27528.0 2.50717
\(495\) 0 0
\(496\) −14200.0 −1.28548
\(497\) −2880.00 4988.31i −0.259931 0.450214i
\(498\) 0 0
\(499\) −4978.00 + 8622.15i −0.446585 + 0.773508i −0.998161 0.0606167i \(-0.980693\pi\)
0.551576 + 0.834125i \(0.314027\pi\)
\(500\) −62.5000 + 108.253i −0.00559017 + 0.00968246i
\(501\) 0 0
\(502\) −648.000 1122.37i −0.0576129 0.0997884i
\(503\) 10656.0 0.944588 0.472294 0.881441i \(-0.343426\pi\)
0.472294 + 0.881441i \(0.343426\pi\)
\(504\) 0 0
\(505\) 8670.00 0.763980
\(506\) 4320.00 + 7482.46i 0.379540 + 0.657383i
\(507\) 0 0
\(508\) −622.000 + 1077.34i −0.0543244 + 0.0940926i
\(509\) −1383.00 + 2395.43i −0.120433 + 0.208596i −0.919939 0.392063i \(-0.871762\pi\)
0.799506 + 0.600659i \(0.205095\pi\)
\(510\) 0 0
\(511\) 4300.00 + 7447.82i 0.372252 + 0.644759i
\(512\) 8733.00 0.753804
\(513\) 0 0
\(514\) 7578.00 0.650294
\(515\) −1130.00 1957.22i −0.0966869 0.167467i
\(516\) 0 0
\(517\) −288.000 + 498.831i −0.0244995 + 0.0424343i
\(518\) −2100.00 + 3637.31i −0.178125 + 0.308521i
\(519\) 0 0
\(520\) −3885.00 6729.02i −0.327632 0.567475i
\(521\) −10530.0 −0.885466 −0.442733 0.896654i \(-0.645991\pi\)
−0.442733 + 0.896654i \(0.645991\pi\)
\(522\) 0 0
\(523\) 12692.0 1.06115 0.530576 0.847637i \(-0.321976\pi\)
0.530576 + 0.847637i \(0.321976\pi\)
\(524\) 1164.00 + 2016.11i 0.0970412 + 0.168080i
\(525\) 0 0
\(526\) −8172.00 + 14154.3i −0.677407 + 1.17330i
\(527\) 5400.00 9353.07i 0.446352 0.773105i
\(528\) 0 0
\(529\) −1116.50 1933.83i −0.0917646 0.158941i
\(530\) 6750.00 0.553210
\(531\) 0 0
\(532\) −2480.00 −0.202108
\(533\) 12210.0 + 21148.3i 0.992259 + 1.71864i
\(534\) 0 0
\(535\) −3510.00 + 6079.50i −0.283646 + 0.491289i
\(536\) 2058.00 3564.56i 0.165843 0.287249i
\(537\) 0 0
\(538\) 3861.00 + 6687.45i 0.309404 + 0.535904i
\(539\) 1368.00 0.109321
\(540\) 0 0
\(541\) 18110.0 1.43920 0.719602 0.694386i \(-0.244324\pi\)
0.719602 + 0.694386i \(0.244324\pi\)
\(542\) −4776.00 8272.27i −0.378500 0.655580i
\(543\) 0 0
\(544\) 1215.00 2104.44i 0.0957586 0.165859i
\(545\) 3685.00 6382.61i 0.289629 0.501653i
\(546\) 0 0
\(547\) −1810.00 3135.01i −0.141481 0.245052i 0.786574 0.617496i \(-0.211853\pi\)
−0.928054 + 0.372445i \(0.878520\pi\)
\(548\) −2118.00 −0.165103
\(549\) 0 0
\(550\) −1800.00 −0.139550
\(551\) 4836.00 + 8376.20i 0.373903 + 0.647619i
\(552\) 0 0
\(553\) 5200.00 9006.66i 0.399867 0.692590i
\(554\) 5943.00 10293.6i 0.455765 0.789408i
\(555\) 0 0
\(556\) −1162.00 2012.64i −0.0886327 0.153516i
\(557\) 14166.0 1.07762 0.538809 0.842428i \(-0.318875\pi\)
0.538809 + 0.842428i \(0.318875\pi\)
\(558\) 0 0
\(559\) 6808.00 0.515112
\(560\) 3550.00 + 6148.78i 0.267884 + 0.463988i
\(561\) 0 0
\(562\) 12429.0 21527.7i 0.932893 1.61582i
\(563\) −6702.00 + 11608.2i −0.501697 + 0.868965i 0.498301 + 0.867004i \(0.333958\pi\)
−0.999998 + 0.00196107i \(0.999376\pi\)
\(564\) 0 0
\(565\) 2715.00 + 4702.52i 0.202161 + 0.350153i
\(566\) 8148.00 0.605099
\(567\) 0 0
\(568\) 6048.00 0.446775
\(569\) −9327.00 16154.8i −0.687185 1.19024i −0.972745 0.231878i \(-0.925513\pi\)
0.285560 0.958361i \(-0.407820\pi\)
\(570\) 0 0
\(571\) 3842.00 6654.54i 0.281581 0.487712i −0.690193 0.723625i \(-0.742475\pi\)
0.971774 + 0.235913i \(0.0758079\pi\)
\(572\) −888.000 + 1538.06i −0.0649111 + 0.112429i
\(573\) 0 0
\(574\) −9900.00 17147.3i −0.719892 1.24689i
\(575\) 3000.00 0.217580
\(576\) 0 0
\(577\) −1726.00 −0.124531 −0.0622654 0.998060i \(-0.519833\pi\)
−0.0622654 + 0.998060i \(0.519833\pi\)
\(578\) −2995.50 5188.36i −0.215565 0.373369i
\(579\) 0 0
\(580\) −195.000 + 337.750i −0.0139602 + 0.0241798i
\(581\) 1560.00 2702.00i 0.111394 0.192939i
\(582\) 0 0
\(583\) 5400.00 + 9353.07i 0.383611 + 0.664434i
\(584\) −9030.00 −0.639836
\(585\) 0 0
\(586\) 18054.0 1.27270
\(587\) 5298.00 + 9176.41i 0.372524 + 0.645231i 0.989953 0.141396i \(-0.0451589\pi\)
−0.617429 + 0.786627i \(0.711826\pi\)
\(588\) 0 0
\(589\) 12400.0 21477.4i 0.867459 1.50248i
\(590\) −180.000 + 311.769i −0.0125601 + 0.0217548i
\(591\) 0 0
\(592\) −2485.00 4304.15i −0.172522 0.298816i
\(593\) −2862.00 −0.198193 −0.0990963 0.995078i \(-0.531595\pi\)
−0.0990963 + 0.995078i \(0.531595\pi\)
\(594\) 0 0
\(595\) −5400.00 −0.372065
\(596\) 129.000 + 223.435i 0.00886585 + 0.0153561i
\(597\) 0 0
\(598\) 13320.0 23070.9i 0.910862 1.57766i
\(599\) −11796.0 + 20431.3i −0.804627 + 1.39365i 0.111916 + 0.993718i \(0.464301\pi\)
−0.916543 + 0.399937i \(0.869032\pi\)
\(600\) 0 0
\(601\) 4787.00 + 8291.33i 0.324902 + 0.562746i 0.981492 0.191501i \(-0.0613355\pi\)
−0.656591 + 0.754247i \(0.728002\pi\)
\(602\) −5520.00 −0.373718
\(603\) 0 0
\(604\) −808.000 −0.0544322
\(605\) 1887.50 + 3269.25i 0.126839 + 0.219692i
\(606\) 0 0
\(607\) −8722.00 + 15106.9i −0.583221 + 1.01017i 0.411874 + 0.911241i \(0.364874\pi\)
−0.995095 + 0.0989273i \(0.968459\pi\)
\(608\) 2790.00 4832.42i 0.186101 0.322336i
\(609\) 0 0
\(610\) −2415.00 4182.90i −0.160296 0.277641i
\(611\) 1776.00 0.117593
\(612\) 0 0
\(613\) −2374.00 −0.156419 −0.0782096 0.996937i \(-0.524920\pi\)
−0.0782096 + 0.996937i \(0.524920\pi\)
\(614\) 13854.0 + 23995.8i 0.910589 + 1.57719i
\(615\) 0 0
\(616\) −5040.00 + 8729.54i −0.329655 + 0.570979i
\(617\) −6081.00 + 10532.6i −0.396778 + 0.687239i −0.993326 0.115338i \(-0.963205\pi\)
0.596549 + 0.802577i \(0.296538\pi\)
\(618\) 0 0
\(619\) −4402.00 7624.49i −0.285834 0.495079i 0.686977 0.726679i \(-0.258937\pi\)
−0.972811 + 0.231600i \(0.925604\pi\)
\(620\) 1000.00 0.0647758
\(621\) 0 0
\(622\) 4608.00 0.297048
\(623\) 10260.0 + 17770.8i 0.659805 + 1.14281i
\(624\) 0 0
\(625\) −312.500 + 541.266i −0.0200000 + 0.0346410i
\(626\) −11013.0 + 19075.1i −0.703144 + 1.21788i
\(627\) 0 0
\(628\) −1189.00 2059.41i −0.0755514 0.130859i
\(629\) 3780.00 0.239616
\(630\) 0 0
\(631\) −12688.0 −0.800478 −0.400239 0.916411i \(-0.631073\pi\)
−0.400239 + 0.916411i \(0.631073\pi\)
\(632\) 5460.00 + 9457.00i 0.343651 + 0.595220i
\(633\) 0 0
\(634\) 5841.00 10116.9i 0.365892 0.633744i
\(635\) −3110.00 + 5386.68i −0.194357 + 0.336636i
\(636\) 0 0
\(637\) −2109.00 3652.90i −0.131180 0.227210i
\(638\) −5616.00 −0.348495
\(639\) 0 0
\(640\) −8295.00 −0.512326
\(641\) −4575.00 7924.13i −0.281906 0.488275i 0.689948 0.723859i \(-0.257633\pi\)
−0.971854 + 0.235583i \(0.924300\pi\)
\(642\) 0 0
\(643\) −12646.0 + 21903.5i −0.775598 + 1.34338i 0.158860 + 0.987301i \(0.449218\pi\)
−0.934458 + 0.356074i \(0.884115\pi\)
\(644\) −1200.00 + 2078.46i −0.0734264 + 0.127178i
\(645\) 0 0
\(646\) 10044.0 + 17396.7i 0.611727 + 1.05954i
\(647\) 2736.00 0.166249 0.0831246 0.996539i \(-0.473510\pi\)
0.0831246 + 0.996539i \(0.473510\pi\)
\(648\) 0 0
\(649\) −576.000 −0.0348382
\(650\) 2775.00 + 4806.44i 0.167453 + 0.290037i
\(651\) 0 0
\(652\) 26.0000 45.0333i 0.00156172 0.00270497i
\(653\) 11109.0 19241.4i 0.665741 1.15310i −0.313343 0.949640i \(-0.601449\pi\)
0.979084 0.203457i \(-0.0652177\pi\)
\(654\) 0 0
\(655\) 5820.00 + 10080.5i 0.347185 + 0.601342i
\(656\) 23430.0 1.39449
\(657\) 0 0
\(658\) −1440.00 −0.0853147
\(659\) 7260.00 + 12574.7i 0.429149 + 0.743309i 0.996798 0.0799625i \(-0.0254801\pi\)
−0.567648 + 0.823271i \(0.692147\pi\)
\(660\) 0 0
\(661\) 5309.00 9195.46i 0.312400 0.541092i −0.666482 0.745521i \(-0.732201\pi\)
0.978881 + 0.204429i \(0.0655339\pi\)
\(662\) 5538.00 9592.10i 0.325137 0.563153i
\(663\) 0 0
\(664\) 1638.00 + 2837.10i 0.0957330 + 0.165814i
\(665\) −12400.0 −0.723085
\(666\) 0 0
\(667\) 9360.00 0.543359
\(668\) −1860.00 3221.61i −0.107733 0.186599i
\(669\) 0 0
\(670\) −1470.00 + 2546.11i −0.0847628 + 0.146813i
\(671\) 3864.00 6692.64i 0.222307 0.385047i
\(672\) 0 0
\(673\) −685.000 1186.45i −0.0392345 0.0679561i 0.845741 0.533593i \(-0.179159\pi\)
−0.884976 + 0.465637i \(0.845825\pi\)
\(674\) 26994.0 1.54269
\(675\) 0 0
\(676\) 3279.00 0.186561
\(677\) −6879.00 11914.8i −0.390519 0.676399i 0.601999 0.798497i \(-0.294371\pi\)
−0.992518 + 0.122098i \(0.961038\pi\)
\(678\) 0 0
\(679\) 2860.00 4953.67i 0.161645 0.279977i
\(680\) 2835.00 4910.36i 0.159878 0.276917i
\(681\) 0 0
\(682\) 7200.00 + 12470.8i 0.404255 + 0.700191i
\(683\) −11988.0 −0.671608 −0.335804 0.941932i \(-0.609008\pi\)
−0.335804 + 0.941932i \(0.609008\pi\)
\(684\) 0 0
\(685\) −10590.0 −0.590691
\(686\) −8580.00 14861.0i −0.477530 0.827107i
\(687\) 0 0
\(688\) 3266.00 5656.88i 0.180981 0.313469i
\(689\) 16650.0 28838.6i 0.920631 1.59458i
\(690\) 0 0
\(691\) −16498.0 28575.4i −0.908268 1.57317i −0.816469 0.577390i \(-0.804071\pi\)
−0.0917997 0.995777i \(-0.529262\pi\)
\(692\) −426.000 −0.0234019
\(693\) 0 0
\(694\) 15732.0 0.860488
\(695\) −5810.00 10063.2i −0.317102 0.549237i
\(696\) 0 0
\(697\) −8910.00 + 15432.6i −0.484204 + 0.838666i
\(698\) 9453.00 16373.1i 0.512609 0.887865i
\(699\) 0 0
\(700\) −250.000 433.013i −0.0134987 0.0233805i
\(701\) 25902.0 1.39558 0.697792 0.716300i \(-0.254166\pi\)
0.697792 + 0.716300i \(0.254166\pi\)
\(702\) 0 0
\(703\) 8680.00 0.465679
\(704\) −5196.00 8999.74i −0.278170 0.481804i
\(705\) 0 0
\(706\) −5121.00 + 8869.83i −0.272991 + 0.472834i
\(707\) −17340.0 + 30033.8i −0.922401 + 1.59765i
\(708\) 0 0
\(709\) 13697.0 + 23723.9i 0.725531 + 1.25666i 0.958755 + 0.284234i \(0.0917392\pi\)
−0.233224 + 0.972423i \(0.574927\pi\)
\(710\) −4320.00 −0.228347
\(711\) 0 0
\(712\) −21546.0 −1.13409
\(713\) −12000.0 20784.6i −0.630299 1.09171i
\(714\) 0 0
\(715\) −4440.00 + 7690.31i −0.232233 + 0.402239i
\(716\) −720.000 + 1247.08i −0.0375805 + 0.0650914i
\(717\) 0 0
\(718\) −7236.00 12533.1i −0.376107 0.651437i
\(719\) −34848.0 −1.80753 −0.903763 0.428033i \(-0.859207\pi\)
−0.903763 + 0.428033i \(0.859207\pi\)
\(720\) 0 0
\(721\) 9040.00 0.466945
\(722\) 12775.5 + 22127.8i 0.658525 + 1.14060i
\(723\) 0 0
\(724\) 1565.00 2710.66i 0.0803353 0.139145i
\(725\) −975.000 + 1688.75i −0.0499456 + 0.0865084i
\(726\) 0 0
\(727\) −14014.0 24273.0i −0.714925 1.23829i −0.962988 0.269543i \(-0.913127\pi\)
0.248063 0.968744i \(-0.420206\pi\)
\(728\) 31080.0 1.58228
\(729\) 0 0
\(730\) 6450.00 0.327021
\(731\) 2484.00 + 4302.41i 0.125683 + 0.217689i
\(732\) 0 0
\(733\) −9001.00 + 15590.2i −0.453560 + 0.785589i −0.998604 0.0528183i \(-0.983180\pi\)
0.545044 + 0.838407i \(0.316513\pi\)
\(734\) −5262.00 + 9114.05i −0.264610 + 0.458318i
\(735\) 0 0
\(736\) −2700.00 4676.54i −0.135222 0.234211i
\(737\) −4704.00 −0.235107
\(738\) 0 0
\(739\) 15284.0 0.760800 0.380400 0.924822i \(-0.375786\pi\)
0.380400 + 0.924822i \(0.375786\pi\)
\(740\) 175.000 + 303.109i 0.00869342 + 0.0150574i
\(741\) 0 0
\(742\) −13500.0 + 23382.7i −0.667925 + 1.15688i
\(743\) −9384.00 + 16253.6i −0.463345 + 0.802538i −0.999125 0.0418201i \(-0.986684\pi\)
0.535780 + 0.844358i \(0.320018\pi\)
\(744\) 0 0
\(745\) 645.000 + 1117.17i 0.0317194 + 0.0549397i
\(746\) −32406.0 −1.59044
\(747\) 0 0
\(748\) −1296.00 −0.0633509
\(749\) −14040.0 24318.0i −0.684927 1.18633i
\(750\) 0 0
\(751\) −4348.00 + 7530.96i −0.211266 + 0.365923i −0.952111 0.305753i \(-0.901092\pi\)
0.740845 + 0.671676i \(0.234425\pi\)
\(752\) 852.000 1475.71i 0.0413155 0.0715605i
\(753\) 0 0
\(754\) 8658.00 + 14996.1i 0.418177 + 0.724305i
\(755\) −4040.00 −0.194743
\(756\) 0 0
\(757\) −38662.0 −1.85627 −0.928134 0.372247i \(-0.878587\pi\)
−0.928134 + 0.372247i \(0.878587\pi\)
\(758\) 2190.00 + 3793.19i 0.104940 + 0.181761i
\(759\) 0 0
\(760\) 6510.00 11275.7i 0.310714 0.538172i
\(761\) 11937.0 20675.5i 0.568615 0.984870i −0.428088 0.903737i \(-0.640813\pi\)
0.996703 0.0811330i \(-0.0258538\pi\)
\(762\) 0 0
\(763\) 14740.0 + 25530.4i 0.699376 + 1.21135i
\(764\) −3576.00 −0.169339
\(765\) 0 0
\(766\) −14616.0 −0.689422
\(767\) 888.000 + 1538.06i 0.0418042 + 0.0724070i
\(768\) 0 0
\(769\) −11809.0 + 20453.8i −0.553763 + 0.959145i 0.444236 + 0.895910i \(0.353475\pi\)
−0.997999 + 0.0632352i \(0.979858\pi\)
\(770\) 3600.00 6235.38i 0.168487 0.291828i
\(771\) 0 0
\(772\) −1333.00 2308.82i −0.0621447 0.107638i
\(773\) −11538.0 −0.536860 −0.268430 0.963299i \(-0.586505\pi\)
−0.268430 + 0.963299i \(0.586505\pi\)
\(774\) 0 0
\(775\) 5000.00 0.231749
\(776\) 3003.00 + 5201.35i 0.138919 + 0.240615i
\(777\) 0 0
\(778\) 21069.0 36492.6i 0.970900 1.68165i
\(779\) −20460.0 + 35437.8i